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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: TOPREAL3:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">r</font>, <font color="Olive" title="b2">r1</font>, <font color="Olive" title="b3">r2</font>, <font color="Olive" title="b4">s1</font>, <font color="Olive" title="b5">s2</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b6">u</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> 2</span>)</span>  st <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Olive" title="b2">r1</font>,<font color="Olive" title="b3">r2</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="metric_1.html#K8" title="METRIC_1:func.8">Ball</a> (<font color="Olive" title="b6">u</font>,<font color="Olive" title="b1">r</font>) &amp; <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Olive" title="b4">s1</font>,<font color="Olive" title="b5">s2</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="metric_1.html#K8" title="METRIC_1:func.8">Ball</a> (<font color="Olive" title="b6">u</font>,<font color="Olive" title="b1">r</font>) &amp;  not <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Olive" title="b2">r1</font>,<font color="Olive" title="b5">s2</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="metric_1.html#K8" title="METRIC_1:func.8">Ball</a> (<font color="Olive" title="b6">u</font>,<font color="Olive" title="b1">r</font>) holds <br/><span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Olive" title="b4">s1</font>,<font color="Olive" title="b3">r2</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="metric_1.html#K8" title="METRIC_1:func.8">Ball</a> (<font color="Olive" title="b6">u</font>,<font color="Olive" title="b1">r</font>)</div></div>
